Lubrication of bearings that are subject to a negative-pressure environment during operation is problematical, since the lubricants generally employed are not vacuum-resistant over the long term and gradually volatilize. Such volatilization occurs regardless of whether lubricating greases or lubricating oils are used and thus lubrication of the contact members of the bearings is not always guaranteed. One consequence of a lack of lubrication is intensified frictional phenomena or "cold welding" between the rolling members and bearing rings, which leads to increased bearing wear and, thus, to a reduced useful life for the bearing. When bearings operate in a vacuum, it is impossible to avoid a lubricant deficiency merely by supplying large amounts of lubricant, because excessive quantities of lubricant lead to an increased formation of lubricant vapor. If these lubricant vapors proceed into the vacuum produced by the pump, they can deteriorate or even contaminate pump components. Moreover, the rotors of vacuum pumps are frequently operated at extremely high speeds, so that excess quantities of lubricant lead to an additional bearing stress. The above described problems are of particular significance in turbomolecular vacuum pumps, whose rotors are operated at 60,000 revolutions per minute and above. Attempts have been previously made to resolve these problems by precisely metering the quantity of lubricant supplied to the bearings. Examples of such solutions are disclosed in German Published Applications 21 19 857, 23 09 665 and 29 47 066.